x2-9x+11=3x

Solution for x2-9x+11=3x equation:

x2-9x+11=3x

We move all terms to the left:

x2-9x+11-(3x)=0

We add all the numbers together, and all the variables

x^2-12x+11=0

a = 1; b = -12; c = +11;
Δ = b2-4ac
Δ = -122-4·1·11
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10}{2*1}=\frac{22}{2}
=11
$